rootmusic

Syntax

Description

W = rootmusic(X,P) returns
the frequencies in radians/sample for the P complex
exponentials (sinusoids) that make up the signal X.

The input X is specified either as:

A row or column vector representing one realization
of signal

A rectangular array for which each row of X represents
a separate observation of the signal (for example, each row is one
output of an array of sensors, as in array processing), such that X'*X is
an estimate of the correlation matrix

The second input argument, P is the number
of complex sinusoids in X. You can specify P as
either:

A positive integer. In this case, the signal subspace
dimension is P.

A two-element vector. In this case, P(2),
the second element of P, represents a threshold
that is multiplied by λmin, the smallest
estimated eigenvalue of the signal's correlation matrix. Eigenvalues
below the threshold λmin*P(2) are
assigned to the noise subspace. In this case, P(1) specifies
the maximum dimension of the signal subspace.

The extra threshold parameter in the second entry in P provides
you more flexibility and control in assigning the noise and signal
subspaces.

The length of the vector W is the computed
dimension of the signal subspace. For real-valued input data X,
the length of the corresponding power vector POW is
given by

length(POW) = 0.5*length(W)

For complex-valued input data X, POW and W have
the same length.

[F, POW]
= rootmusic(...,Fs) returns
the vector of frequencies F calculated in Hz.
You supply the sampling frequency Fs in Hz. If
you specify Fs with the empty vector [],
the sampling frequency defaults to 1 Hz.

[W,POW]
= rootmusic(...,'corr') forces the input argument X to
be interpreted as a correlation matrix rather than a matrix of signal
data. For this syntax, you must supply a square matrix for X,
and all of its eigenvalues must be nonnegative. You can place the 'corr' option
anywhere after the P input argument.

Note

Examples

Sinusoid Amplitudes

Estimate the amplitudes for two sinusoids in noise. The separation between the sinusoids is less than the resolution of the periodogram, radians/sample. Use the autocorrelation matrix as the input to rootmusic.

Diagnostics

If the input signal, x is real and an odd
number of sinusoids, p is specified, the following
error message is displayed:

Real signals require an even number p of complex sinusoids.

Algorithms

The MUSIC algorithm used by rootmusic is
the same as that used by pmusic.
The algorithm performs eigenspace analysis of the signal's correlation
matrix in order to estimate the signal's frequency content.

The difference between pmusic and rootmusic is:

pmusic returns the pseudospectrum
at all frequency samples.

rootmusic returns the estimated
discrete frequency spectrum, along with the corresponding signal power
estimates.

rootmusic is most useful for frequency estimation
of signals made up of a sum of sinusoids embedded in additive white
Gaussian noise.